5. method of inferences ifk15037, 3 credits - yuita arum...

5.METHODOFINFERENCESIFK15037,3credits

YUITAARUMSARI,S.Kom,[email protected]

1

OUTLINE

YuitaArumSari,S.Kom,M.Kom 2

Tree Graph La,ce

Forward&BackwardChaining

Logic,Syllogism,

ModusPonens

ShallowandCasual

Reasoning

OtherInferenceMethod

YuitaArumSari,S.Kom,M.Kom3

Tree

ExpertSystems:PrinciplesandProgramming,FourthEdi:on

v  A tree is a hierarchical data structure consisting of: v Nodes – store information v Branches – connect the nodes

v  The top node is the root, occupying the highest hierarchy. v  The leaves are at the bottom, occupying the lowest hierarchy. v  Every node, except the root, has exactly one parent. v  Every node may give rise to zero or more child nodes. v  A binary tree restricts the number of children per node to a

maximum of two. v  Degenerate trees have only a single pathway from root to its

one leaf.


Tree



Graph


Ø Graphs are sometimes called a network or net. Ø A graph can have zero or more links between nodes – there is

no distinction between parent and child. Ø  Sometimes links have weights – weighted graph; or, arrows –

directed graph. Ø  Simple graphs have no loops – links that come back onto the

node itself. Ø A circuit (cycle) is a path through the graph beginning and

ending with the same node.

Ø Acyclic graphs have no cycles.

Ø Connected graphs have links to all the nodes.

Ø Digraphs are graphs with directed links.

Ø  Lattice is a directed acyclic graph.


SimpleGraph



MakingDecision


Trees/la,cesareusefulforclassifyingobjectsinahierarchicalnature.

Trees/la,cesareusefulformakingdecisions.

Werefertotrees/la,cesasstructures.

DecisiontreesareusefulforrepresenFngandreasoningaboutknowledge.


BinaryDecisionTree


EveryquesFontakesusdownonelevelinthetree.

• Allleaveswillbeanswers.• AllinternalnodesarequesFons.• Therewillbeamaximumof2NanswersforNquesFons.

AbinarydecisiontreehavingNnodes:

Decisiontreescanbeselflearning.

DecisiontreescanbetranslatedintoproducFonrules.


DecisionTreeExample



StateandProblemSpaces


Astatespacecanbeusedtodefineanobject’sbehavior.

DifferentstatesrefertocharacterisFcsthatdefinethestatusoftheobject.

AstatespaceshowsthetransiFonsanobjectcanmakeingoingfromonestatetoanother.


StateandProblemSpaces


AFSMisadiagramdescribingthefinitenumberofstatesofamachine.

AtanyoneFme,themachineisinoneparFcularstate.

Themachineacceptsinputandprogressestothenextstate.

FSMsareoYenusedincompilersandvaliditycheckingprograms.


UsingFSMtoSolveProblem


Characterizingill-structuredproblems–one

havinguncertainFes.

Well-formedproblems:

•  Explicitproblem,goal,andoperaFonsareknown

•  DeterminisFc–wearesureofthenextstatewhenanoperatorisappliedtoastate.

•  Theproblemspaceisbounded.•  Thestatesarediscrete.


StateDiagramExample


State Diagram for a Soft Drink Vending Machine Accepting Quarters (Q) and Nickels (N)


AND-ORTreeandGoals


Ø 1990s, PROLOG was used for commercial applications in business and industry.

Ø PROLOG uses backward chaining to divide problems into smaller problems and then solves them.

Ø AND-OR trees also use backward chaining.

Ø AND-OR-NOT lattices use logic gates to describe problems.


TypesofLogic


§  Deduction – reasoning where conclusions must follow from premises

§  Induction – inference is from the specific case to the general

§  Intuition – no proven theory

§  Heuristics – rules of thumb based on experience

§  Generate and test – trial and error §  Abduction – reasoning back from a true condition to the

premises that may have caused the condition §  Default – absence of specific knowledge §  Autoepistemic – self-knowledge §  Nonmonotonic – previous knowledge §  Analogy – inferring conclusions based on similarities with other

situations


DeducWveLogic


Argument–groupofstatementswherethelastisjusFfiedonthebasisofthepreviousones

DeducFvelogiccandeterminethevalidityofanargument.

Syllogism–hastwopremisesandoneconclusion

DeducFveargument–conclusionsreachedbyfollowingtruepremisesmustthemselvesbetrue


SyllogismvsRules


Syllogism: All basketball players are tall. Jason is a basketball player. � Jason is tall.

IF-THEN rule:

IF All basketball players are tall and Jason is a basketball player THEN Jason is tall.


CategoricalSyllogism


Premises and conclusions are defined using categorical statements of the form:


CategoricalSyllogism



RuleofInference


Ø Venn diagrams are insufficient for complex arguments. Ø Syllogisms address only a small portion of the possible logical

statements. Ø Propositional logic offers another means of describing arguments.

1.  If a class is empty, it is shaded. 2.  Universal statements, A and E are always drawn before

particular ones. 3.  If a class has at least one member, mark it with an *. 4.  If a statement does not specify in which of two adjacent

classes an object exists, place an * on the line between the classes.

5.  If an area has been shaded, not * can be put in it.

Proving the validity of syllogistic arguments using Venn Diagram


DirectReasoning-ModusPonens


Modusponensisnecessarybecauseitshowsabasicrule-basedexpertsystems


RulesofInference



TheModusMeanings

ThecondiFonalanditsVariant



LimitaWonsofPreposiWonalLogic

Ifanargumentisinvalid,itshouldbeinterpretedassuch–thattheconclusionisnecessarilyincorrect.

Anargumentmaybeinvalidbecauseitispoorlyconcocted.

AnargumentmaynotbeprovableusingproposiFonallogic,butmaybeprovableusingpredicatelogic.



ShallowandCausalReasoning

ExperienFalknowledgeisbasedonexperience.

Inshallowreasoning,thereisli`le/nocausalchainofcauseandeffectfromoneruletoanother.

Advantageofshallowreasoningiseaseofprogramming.

Framesareusedforcausal/deepreasoning.

Causalreasoningcanbeusedtoconstructamodelthatbehavesliketherealsystem.



Chaining

Chain–agroupofmulFpleinferencesthatconnectaproblemwithitssoluFon

Achainthatissearched/traversedfromaproblemtoitssoluFoniscalledaforwardchain.

Achaintraversedfromahypothesisbacktothefactsthatsupportthehypothesisisabackwardchain.

Problemwithbackwardchainingisfindachainlinkingtheevidencetothehypothesis.



CausalForwardChaining



SomeCharacterisWcFCandBC



SomeCharacterisWcFCandBC


Analogy–relaFngoldsituaFons(asaguide)tonewones.

Generate-and-Test–generaFonofalikelysoluFonthentesttoseeifproposedmeetsallrequirements.

AbducFon–FallacyoftheConverse

NonmonotonicReasoning–theoremsmaynotincreaseasthenumberofaxiomsincrease.


TypesodInference



Metaknowledge


v The Markov decision process (MDP) is a good application to path planning.

v In the real world, there is always uncertainty, and pure logic is not a good guide when there is uncertainty.

v A MDP is more realistic in the cases where there is partial or hidden information about the state and parameters, and the need for planning.


REFERENCES

•  Joseph C. Giarratano, Gary D. Riley, Expert Systems: Principles and Programming, Published November 14th 2004 by Course Technology Inc.

YuitaArumSari,S.Kom,M.Kom 33

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5. method of inferences ifk15037, 3 credits - yuita arum...

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